1. Field of the Invention
The present invention relates generally to signal transformation and in particular to signal transformation for scanning.
2. Background Information
Precise positioning is the enabling technology for a variety of applications ranging from scanning probe microscopy and semiconductor manufacturing systems to data storage devices. With the advent of nanotechnology and bio-nanotechnology, applications of precise positioning have further increased. Positioners such as piezo-electric flexure stages and MEMS micro-scanners are widely employed to perform fast scan operations in these devices. Fast scan operations inevitably require the design of high bandwidth controllers.
However, high bandwidth controllers cause closed-loop systems to be susceptible to measurement noise. This significantly impacts the positioning accuracy, thus defeating the purpose of using a highly precise positioner in the first place. Low bandwidth controllers on the other hand would not be able to track the high frequency content reference signals. This is a fundamental limitation in a one-degree of freedom linear control system. In a one-degree of freedom linear control system, the reference tracking transfer function relating the position with the reference signal is equal to the noise sensitivity transfer function relating the position with the measurement noise.
Within the framework of feedback control, there are two conventional linear system approaches that are typically employed. One is to shape the reference signal so as to reduce the high frequency content. In the case of a triangular reference signal, which is widely preferred, this amounts to performing a sine-cap at the turn arounds. This approach does not significantly affect the frequency content of the desired reference signal without deteriorating the quality of the signal. Another approach is to design a higher degree of order controllers which are not bound by the above constraint. Even then, a complete decoupling is not possible.